Question: If $x \barwedge y = 4x^{2}-y^{2}$ and $x \dagger y = 4x-3y$, find $(-4 \dagger -6) \barwedge 4$.
Answer: First, find $-4 \dagger -6$ $ -4 \dagger -6 = (4)(-4)-(3)(-6)$ $ \hphantom{-4 \dagger -6} = 2$ Now, find $2 \barwedge 4$ $ 2 \barwedge 4 = 4(2^{2})-4^{2}$ $ \hphantom{2 \barwedge 4} = 0$.